Consider the set S of points in the plane consisting of the ordered pairs (i, j), where 1 6 i 6 m and 1 6 j 6 n. A problem related to the study of segmentation evaluation of visual images concerns finding a permutation σ of the points of S for which the sum

1. Introducing the birank. A partition is defined as being a nonincreasing sequence of positive integers, λ = (λ1,λ2, . . . ,λr ). The set of all partitions, which includes the empty partition ∅, is denoted by . The sum of the parts of a given partition is called the weight of the partition, wt(λ) = λ1+λ2+···+λr . It is standard notation to write (z;q)∞ := ∏ t≥0(1−zq) and p−k(n) for the coeffic...

R l definable in R such that F (t) = G(t, F (t)) for all t ∈ (a, b) and each component function Gi : R 1+l → R is independent of the last l− i variables (i = 1, . . . , l). If R is o-minimal and F : (a, b) → R is R-Pfaffian, then (R, F ) is o-minimal (Proposition 7). We say that F : R → R is ultimately R-Pfaffian if there exists r ∈ R such that the restriction F ↾(r,∞) is R-Pfaffian. (In genera...

In this paper, the new concept of near PS-compactness in L-topological spaces is introduced. It is defined for any L-subset. Its characterizations and topological properties are systematically studied. And the relationship is exposed between near PScompactness and PS-compactness, and also fuzzy compactness. 2003 Elsevier Inc. All rights reserved.

Consider a linear stochastic differential equation dX(t) = (aX(t) + bX(t− 1))dt+ dW t , t ≥ 0 with time delay driven by a fractional Brownian motion {WH t , t ≥ 0}. We investigate the asymptotic properties of the maximum likelihood estimator of the parameter θ = (a, b).

In this paper we study the problem of constructing sets of s latin squares of order m such that the average number of different ordered pairs obtained by superimposing two of the s squares in the set is as large as possible. We solve this problem (for all s) when m is a prime power by using projective planes. We also present upper and lower bounds for all positive integers m.

The articles [9], [5], [11], [1], [10], [6], [3], [4], [2], [8], [12], and [7] provide the notation and terminology for this paper. We introduce metric structures which are extensions of 1-sorted structure and are systems 〈 a carrier, a distance 〉, where the carrier is a set and the distance is a function from [: the carrier, the carrier :] into R. One can check that there exists a metric struc...

We determine all triples (a, b, n) of positive integers such that a and b are relatively prime and nk divides an+bn (respectively, an bn), when k is the maximum of a and b (in fact, we answer a slightly more general question). As a by-product, we see that, for m,n 2 N+ with n 2, nm divides mn + 1 if and only if (m,n) = (2, 3) or (1, 2), which generalizes problems from the 1990 and 1999 editions...

The issue of shared use urban freight facilities first received attention during the 1970's when it was observed that, while inter-urban freight movements were becoming increasingly efficient, there were significant diseconomies in the movement of freight via truck within urban areas. Early research suggested that shared urban freight facilities should be constructed so that trucking companies ...

2. Cycles and their terminology. Let L be an n Xn Latin square or, alternatively, let Q be a quasigroup of order n. Let M be the set of n2 ordered triplets ijk, where k is the entry in the ith row and jth column of L. If 5 is the set of n2 ordered pairs ij, and if 7r,:Af—>S is the projection parallel to the ith coordinate (for example, ir2(ijk) = ik), then for each i, l^i^3, t< is onto S (or eq...